We have 14 seats on two vans and there are 9 boys and 3 girls
i.e total 12 peoples
The number of ways of arranging 12 peoples on 14 seats without restriction is 14P12
14P12 = \(\frac{14!}{2!}\) = \(\frac{17∙13!}{2!}\)
= 7 × 13! Ways.
Three girls can be seated together in back row on adjacent seats in the following ways
1,2,3, or 2,3,4 of first van
1,2,3 or 2,3,4 of second van
In each way the three girls can interchange among themselves in 3! Ways
∴ total number of ways in which 3 girls 3 girls sit together in a back row = 4 × 3! = 24 ways
9 boys are to seated on 11 seats = 11P9 = \(\frac{11!}{2!}\)
Hence, the total number of ways \(\frac{24\times11}{2!}\) = 12 × 11!